Delivered over the tannoy at 7.45pm, it was an irresistible invitation: “There’s a lovely pod of walruses over on the beach, belching and farting and waiting for us to come, so I urge everyone to get over there. The last zodiac back will be at 11 o’clock.”

A quarter of an hour later, layered and lifejacketed, some 60 of us, expedition staff as well as passengers of the good ship Polar Pioneer, were swinging our legs over the gunwales of the zodiacs at the remains of the 17th-century Dutch whaling station of Smeerenburg (“Blubber Town”), on the north-west coast of the island of Spitsbergen. The walruses were still several hundred yards away from us, on the other side of a sand spit , but the sun was so strong, the air so clear, that we could see the ivory gleam of their tusks. Following a briefing from our expedition leader, Gary Miller (“By law, we can get no closer than 30m”), we advanced slowly towards them.

About 35 of them were hauled up on the sand, lying any old way over the top of one another. Through binoculars, we watched as snores and yawns from the mouth of one lifted the tail of another. In an inlet to the right of them, a few old warriors, one armed with only the stumps of its tusks, swam obligingly backwards and forwards between sandy beach and snow-dusted peaks, till even the keenest of photographers was sated.

"Delivered over the tannoy at 7.45pm, it was an irresistible invitation: 'There’s a lovely pod of walruses over on the beach, belching and farting and waiting for us to come, so I urge everyone to get over there.'"

We had boarded at the northern Icelandic port of Isafjordur, to sail up the east coast of Greenland and on to Spitsbergen. Our ship was a former Russian research vessel, crewed by Russians but chartered by the Australian company Aurora Expeditions. Fellow passengers were mostly retired Australians. A younger contingent included an Army helicopter pilot and three Americans, one an internet entrepreneur and the other two working on satellite systems for Lockheed. We had been drawn by the promise of “fantastic icebergs and a fairytale landscape of granite spires rising 1,000m above the fjords” – and by the possibility of seeing polar bears.

We got our first and only (confirmed) sighting of a bear on our first full day aboard the ship. A group of us were on the bridge (open to passengers throughout the voyage) when Gary spotted it through binoculars: “Two o’clock to the ship. Walking along a ridge. There’s a little hut on top and it’s to the left of that.”

Polar bears remained mostly elusive on this cruise although live throughout the Arctic region (Alamy) Photo: Alamy

Some others got a glimpse, and then Gary’s voice over the tannoy was encouraging everyone to put on their thermals, wellies and lifejackets and board the zodiacs for a closer look from just offshore. That’s the trouble with polar bears: when you know there’s one about, you also know it’s not safe to make a landing. We cruised up and down for a while, but the bear, intent on a nap, and too far away to be more than a speck at the end of the longest lens, made no further movement but a brief turn of its head towards us.

We would see plenty of other wildlife on the trip. From zodiacs we would have one good view at close quarters of bearded seals, hauled out on a low-lying iceberg, and occasional glimpses, in the distance, of ringed seals and harp seals. Ashore, we would enjoy regular sightings of the musk ox and the Arctic hare. The former, hard initially to separate from the terrain, was all rippling shoulders and cream legs, like a bison in gaiters. The latter was a startling white against the earthy tones of the tundra. Had it been wearing a waistcoat and consulting a fobwatch, like the White Rabbit in Tenniel’s illustrations for Alice in Wonderland, it couldn’t have looked more conspicuous. If we had been told on Day 1, however, that that would be our one and only polar bear sighting, some, I think, might have wondered whether the trip would be value for money. By the end of our two weeks there wasn’t a passenger among the 50 on board who felt at all short-changed. Quite the opposite.

The Arctic is a place that makes children of us again. It’s a place where you reassess what you thought you knew. I used to think I was pretty good at estimating distances. On one outing Graeme “Snowy” Snow was driving our zodiac towards the face of a glacier. It seemed to me somewhere between 500 and 1,000 yards off. How far away is it, I asked. “Oh, I’d say about four miles,” he answered.

It was the same with icebergs which in our minds we turned into the Guggenheim Bilbao or a medieval castle. Seeing one on its own, we’d guesstimate its size. Then a 10-person zodiac or a single-man kayak would glide in front, and we’d realise we’d underestimated its mass by – I don’t know – maybe a factor of five or 10.

I learnt a new vocabulary. Ice can be, among other things, brash (floating fragments), frazil (fine plates, suspended in water), grease (a stage beyond frazil, forming a soupy layer), nilas (a thin crust that bends in waves and swells) and pancake (circular pieces with raised rims, formed from the freezing-together of grease or the breaking-up of nilas).

The Arctic is a place where you realise how deceitful was the colouring of the “frozen waste” in your school atlas, and how the cliffs of a Greenland fjord (Narwhal Sund), reddened by a powerful evening sun, could double in a location shoot for Egypt’s Valley of the Kings. Ashore , you discover that what looked brown from the ship is bright with the red flowers of rose root, the violet of Arctic harebell and the yellow and orange of lichens.

The Arctic is a place, too, where you throw yourself out of bed at 1.45am because you’ve heard other people go by your cabin and you’re frightened that you might miss something. That’s what many of us, most of us, did as our ship sailed through the summer’s last frontier of pack ice between Greenland and Spitsbergen.

I climbed to the bridge to find most of our team already there, binoculars trained on the ice. What drew us was possibility. “You might,” said Carol Knott, the ship’s historian, “see bear prints on a floe or drag lines where a seal has hauled itself up. Very, very occasionally you might see a red stain where a seal has been killed by a bear.”

What kept us there, hour after hour, when PPB (possible polar bear) after PPB had turned to nought, was the pink of the dawn light, the occasional flash of a minke whale fin, the skim of a fulmar over a floe, and the quietly mesmerising movement of the pack ice, the fragments bumping inwards and then outwards as if a cackhanded giant were trying to assemble a badly sawn jigsaw puzzle.

"The polar bear, throughout our trip, was always just offstage."

The polar bear, throughout our trip, was always just offstage. Everywhere we landed we would wait at the shore while our guides, equipped with guns and flares, satisfied themselves that there wasn’t a bear just beyond the first ridge or round the first bend. Then we’d set off through the springy tundra, one group staying close to the shore, one following a medium walk and one a long walk of anything up to three hours, usually loping in pursuit of Howard Whelan (who led photographic expeditions to Antarctica that resulted in the film Happy Feet). The bergs were as pregnant with possibility as the bears. We heard lots of booms, witnessed several cracks and rolls and felt the last ripples of waves that might have done damage had we been closer when they were unleashed.

At Blomsterbugten (Flower Bay), in Franz Joseph Fjord in eastern Greenland, we came back from a walk to find we’d missed a drama. A big berg in the bay, which the kayakers had passed earlier in the day, had split in two, sending a wave crashing to shore that swamped our moored zodiacs and one photographer’s backpack.

Ann Ward, the ship’s doctor, and several others had been looking at the berg as it rocked backwards and forwards, but hadn’t expected it to shed ice. She showed me a video she had been shooting on her compact camera, the last of it upside down as she started running in response to Gary’s shout of “S***! Get the gear!”

It wasn’t often we saw our guides flustered. They were, indeed, intimidatingly multi-competent, one minute briefing us in the lecture room on paleolithic Inuit settlements or Arctic seabirds, the next easing a zodiac through the bergs while pointing out seals and seabirds. When their guiding was done, they’d help their catering colleagues to dry dishes in the galley or serve drinks behind the bar.

The Polar Pioneer ship in Spitsbergen

Their team spirit was embraced by the passengers, too, who quickly became a group, bonding in the dining room over meals that ranged from vegetable burritos to braised lamb shanks. There, were, though two sub-groups: everyone else marvelled at the endurance of the kayakers (nearly nine miles on their first day and a total close to 100 for the trip); and was mystified by the “serious” photographers (why did they need those suitcase-sized kitbags, and how could they spend so long in front of a single iceberg?).

No one minded being out of mobile-phone range . We had a connection, briefly, during our day at the only inhabited place where we landed, Ittoqqortoormiit (population: 450 East Greenlanders and 150 sled dogs), where the Lutheran pastor gave us a graphic illustration of what climate change is doing. The permafrost under his church, built around 1938, is cracking and the building is doing the same, listing like a ship in a storm.

Global warming and its effects cropped up a few times in the talks and presentations with which our team filled the days spent at sea, but there was no tub-thumping about it. It was as if Aurora’s staff believed that showing us the wonders of the Arctic, and what was worth conserving there, would turn us all into passionate conservationists. They were probably right.

On our last day aboard , with the glacier of Lilliehook booming and cracking all round us , 16 of my fellow passengers, with five staff and crew, volunteered to take “the polar plunge”. One after another, either down a gangway or over the deck, they went in, while between their jumps Gary and Snowy, standing in a zodiac below, nudged patches of ice away from the hull of the ship.

“Well done, everyone,” said

Robyn Mundy , the assistant expedition leader, over the tannoy. “Sixteen lunatics throwing themselves off a perfectly good ship.” And three of them did it in the nude. They were, in their own way, answering the call of the cold.